Abstract. Reynolds ’ notion of relational parametricity has been extremely influential and well studied for polymorphic type theories such as System F. The extension of relational parametricity to higher kinded polymorphism, which allows quantification over type operators as well as types, has not been as well studied. In this paper we give a model of relational parametricity for System F ω and investigate some of its consequences. 1

Free theorems are a charm, allowing the derivation of useful statements about programs from their (polymorphic) types alone. We show how to reap such theorems not only from polymorphism over ordinary types, but also from polymorphism over type constructors restricted by class constraints. Our prime application area is that of monads, which form the probably most popular type constructor class of Haskell. To demonstrate the broader scope, we also deal with a transparent way of introducing difference lists into a program, endowed with a neat and general correctness proof.